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arXiv:1901.04466 · Physical Review Letters

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices

Chuanchang Zeng, Tudor D. Stanescu, Chuanwei Zhang, V. W. Scarola, Sumanta Tewari

Published Aug 6, 2019• 49 citations
arXivHTMLPDF

Abstract

Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.

DOI
10.1103/physrevlett.123.060402

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Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.
Topological superfluids protected by mirror and time-reversal symmetries are exotic states of matter possessing Majorana Kramers pairs (MKPs), yet their realizations have long been hindered by the requirement of unconventional pairing. We propose to realize such a topological superfluid by utilizing s-wave pairing and emergent mirror and time-reversal symmetries in two coupled 1D ultracold atomic Fermi gases with spin-orbit coupling. By stacking such systems into 2D, we discover topological and Dirac-nodal superfluids hosting distinct MKP flat bands. We show that the emergent symmetries make the MKPs and their flat bands stable against pairing fluctuations that otherwise annihilate Majorana pairs. Exploiting new experimental developments, our scheme provides a unique platform for exploring MKPs and their applications in quantum computation.
A Majorana zero bound mode exists in the vortex core of a chiral p+ipp+ipp+ip superconductor or superfluid, which can be driven from an sss-wave pairing state by two-dimensional spin-orbit coupling. We propose here a novel scheme based on realistic cold atom platforms to generate two-dimensional spin-orbit interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work may open a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.
Proximity-induced superconductivity in low-dimensional systems offers a powerful pathway to engineer topological superconducting phases in, otherwise, non-superconducting systems. These exotic phases are of fundamental and technological interest due to the presence of robust zero-energy modes, the Majorana bound states. In this work, we propose a theoretical framework to realize Majorana bound states from the edge states of a two-dimensional semi-Dirac system. This anisotropic system, under specific conditions, can host non-chiral edge states that propagate only along particular edges, effectively forming separated one-dimensional channels. We show that the interplay between Rashba spin-orbit coupling and a Zeeman field on this setup provides the right conditions to get an effective p-wave pairing between the edge states by proximity with a s-wave superconductor. In finite geometries, each edge can independently undergo a topological phase transition into a one-dimensional topological superconductor and give rise to four zero-energy modes localized at the strip corners. At low energies, the edge states subspace admits a description in terms of coupled Kitaev chains, providing a clear picture of the origin, robustness, and tunability of the corner Majorana modes. Our results establish semi-Dirac materials as a natural platform for realizing Majorana modes in two dimensions without relying on engineered nanostructures, vortices, or crystalline higher-order topology.
We propose a method to prepare Majorana pairs at the corners of imprinted defects on a two-dimensional cold-atom optical lattice with sss-wave superfluid pairing. Different from previous proposals that manipulate the effective Dirac masses, our scheme relies on the sign flip of the spin-orbit coupling at the corners, which can be tuned in experiments by adjusting the angle of incident Raman lasers. The Majorana corner pairs are found to be located at the interface between two regimes with opposite spin-orbit coupling strengths in an anticlockwise direction and are robust against certain symmetry-persevered perturbations. Our work provides a way for implementing and manipulating Majorana pairs with existing cold-atom techniques.
Abstract We explore the topological phase, which involves Majorana type topological zero mode fermions (MTZFs) at the edge, using d–wave superfluid with Rashba spin-orbit coupling (SOC) interactions. The self-Hermitian of this MTZF( γ†(k)=γ(k){{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}{\boldsymbol{=}}{\boldsymbol{\gamma }}{\boldsymbol{(}}{\bf{k}}{\boldsymbol{)}}γ†(k)=γ(k) γ † ( k ) = γ ( k ) ) is similar to that of the Majorana fermions (MFs) ( γ†=γ{{\boldsymbol{\gamma }}}^{{\boldsymbol{\dagger }}}={\boldsymbol{\gamma }}γ†=γ γ † = γ ). We show that, to realize a single MTZF at each edge in superfluid with d–wave pairing in a Majorana type Kramers Doublet (MTKD) state, it is important to lift both the spin and the Dirac Cones degeneracies. These non-Abelian anyons obey the non-Abelian statistics which may be useful to realize topological quantum computation. We suggest that the topological feature could be tested experimentally in superfluids of cold fermionic atoms with laser field induced spin orbit interactions. These studies give a new possible way to investigate the MTZFs in a two-dimensional (2D) system as compared to MFs in the one-dimensional (1D) nano-wire and 2D system, and enrich the theoretical research on finding non-Abelian anyons in topological system.
We theoretically investigate the behavior of dark solitons in a one-dimensional spin-orbit coupled atomic Fermi gas in harmonic traps by solving self-consistently the Bogoliubov--de Gennes equations. The dark soliton---to be created by phase imprinting in future experiments---is characterized by a real order parameter, which changes sign at a point node and hosts localized Andreev bound states near the node. By considering both cases of a single soliton and multiple solitons, we find that the energy of these bound states decreases to zero when the system is tuned to enter the topological superfluid phase by increasing an external Zeeman field. As a result, two Majorana fermions emerge in the vicinity of each soliton, in addition to the well-known Majorana fermions at the trap edges associated with the nontrivial topology of the superfluid. We propose that the soliton-induced Majorana fermions can be directly observed by using spatially resolved radio-frequency spectroscopy or indirectly probed by measuring the density profile at the point node. For the latter, the deep minimum in the density profile will disappear due to the occupation of the soliton-induced zero-energy Majorana fermion modes. Our prediction could be tested in a resonantly interacting spin-orbit coupled 40K{}^{40}\text{K}40K Fermi gas confined in a two-dimensional optical lattice.